coordination of growth rate, cell cycle, stress response ...airoldi/pub/journals/j007...et al.,...

Molecular Biology of the CellVol. 19, 352–367, January 2008

Coordination of Growth Rate, Cell Cycle, Stress Response,and Metabolic Activity in YeastMatthew J. Brauer,*†‡ Curtis Huttenhower,*§� Edoardo M. Airoldi,*§�Rachel Rosenstein,*¶ John C. Matese,* David Gresham,*† Viktor M. Boer,*†Olga G. Troyanskaya,*§ and David Botstein*†

*Lewis-Sigler Institute for Integrative Genomics and Departments of †Molecular Biology and §ComputerScience, Princeton University, Princeton, NJ 08544; and ¶School of Medicine, Yale University, New Haven, CT06510

Submitted August 14, 2007; Revised October 4, 2007; Accepted October 11, 2007Monitoring Editor: Thomas Fox

We studied the relationship between growth rate and genome-wide gene expression, cell cycle progression, and glucosemetabolism in 36 steady-state continuous cultures limited by one of six different nutrients (glucose, ammonium, sulfate,phosphate, uracil, or leucine). The expression of more than one quarter of all yeast genes is linearly correlated with growthrate, independent of the limiting nutrient. The subset of negatively growth-correlated genes is most enriched forperoxisomal functions, whereas positively correlated genes mainly encode ribosomal functions. Many (not all) genesassociated with stress response are strongly correlated with growth rate, as are genes that are periodically expressed underconditions of metabolic cycling. We confirmed a linear relationship between growth rate and the fraction of the cellpopulation in the G0/G1 cell cycle phase, independent of limiting nutrient. Cultures limited by auxotrophic requirementswasted excess glucose, whereas those limited on phosphate, sulfate, or ammonia did not; this phenomenon (reminiscentof the “Warburg effect” in cancer cells) was confirmed in batch cultures. Using an aggregate of gene expression values, wepredict (in both continuous and batch cultures) an “instantaneous growth rate.” This concept is useful in interpreting thesystem-level connections among growth rate, metabolism, stress, and the cell cycle.

INTRODUCTION

The most fundamental system-level challenge for cell phys-iology, especially for microorganisms, is the achievement ofbalanced growth in the face of a fluctuating environment. Avariety of cellular processes, carried out by proteins ex-pressed from thousands of genes, have to be coordinated toallow cells to efficiently reproduce, grow and compete forresources. Among the processes that have to be coordinatedare the extraction of energy and metabolites from the envi-ronment; biosynthesis of appropriate amounts of hundredsof molecules large and small; and the events of the celldivision cycle, including replication of the DNA and assem-bly and segregation of subcellular organelles and structures.All of this coordination has to be done in such a way as toallow the cell to modify its activities, often on a very shorttime scale, when the environment changes.

The goal of understanding how cells achieve balancedgrowth (or growth homeostasis) has been pursued since themiddle of the 20th century, and much progress has beenmade. In today’s textbooks, one can find coherent (if not

quite comprehensive) accounts of metabolic regulation of allkinds: regulation of macromolecular synthesis, control of thecell cycle, assembly and distribution of organelles, and re-sponse of these processes to all kinds of environmentalperturbations and stresses. However, until recently, therehave been no ways of following the expression of all genesat once. Of necessity, therefore, progress has been made byfocusing on the roles of individual genes in each process,often through mutations in them. In the last decade, mi-croarray technology has allowed genome-scale gene expres-sion studies of the yeast cell cycle (Cho et al., 1998; Spellmanet al., 1998; Pramila et al., 2006; Kudlicki et al., 2007); theresponse to various stresses (Gasch et al., 2000; Gasch et al.,2001), and a variety of metabolic circumstances, such as thediauxic shift from growth on glucose to growth on ethanol(DeRisi et al., 1997; Brauer et al., 2005) and growth at steadystate in a variety of limiting nutrients (Boer et al., 2003;Saldanha et al., 2004; Regenberg et al., 2006; Castrillo et al.,2007). A couple of recent studies (Klevecz et al., 2004; Tu etal., 2005) examined gene expression during oscillatory be-havior in chemostats, from which emerged a potential con-nection with cell cycle control (Futcher, 2006).

We sought to explore, systematically and quantitatively,the relationship between the growth rate and genome-widepatterns of gene expression in exponentially growing, nom-inally unstressed yeast cultures. We specifically sought todetermine which (if any) yeast genes are expressed at a level(measured as mRNA concentration using DNA microarrays)simply correlated to a cell’s growth rate, independent of theenvironmental factors that ultimately mandate the observedinstantaneous growth rate. In addition to gene expression,we measured the fraction of unbudded cells (i.e., in the

This article was published online ahead of print in MBC in Press(http://www.molbiolcell.org/cgi/doi/10.1091/mbc.E07–08–0779)on October 24, 2007.� These authors contributed equally to this work.‡ Present address: Genentech, Inc., 1 DNA Way, South San Fran-cisco, CA 94080.

Address correspondence to: David Botstein ([email protected]).

352 © 2007 by The American Society for Cell Biology

G0/G1 stages of the cell cycle) and the concentrations ofglucose and ethanol in the media.

Like other recent studies (Regenberg et al., 2006; Castrilloet al., 2007), we exploited the chemostat continuous culturesystem (Monod, 1950; Novick and Szilard, 1950) to providesteady-state conditions at different constant growth rates ina variety of media where the growth rate-limiting nutrient isknown. The chemostat allows one to control the growth rateof the organism by adjusting the flow rate of fresh mediuminto the growth chamber providing a defined environmentamenable to genome-scale analyses (Hoskisson and Hobbs,2005).

By analyzing mRNA abundance data we obtained from 36chemostat cultures (six different limiting nutrients each atsix different growth rates), we found that a surprisinglylarge fraction (�27%) of all yeast genes are expressed (asmeasured by relative mRNA abundance) in a way that isclosely correlated (either negatively or positively) with thegrowth rate of the culture. We verified quantitatively, andextended to the conditions of steady-state culture, the rela-tionship between growth rate and the fraction of unbuddedcells first suggested by Unger and Hartwell (1976). We alsodiscovered a striking difference between growth limitationby ammonium, sulfate, or phosphate (“natural nutrients”; cf.Saldanha et al., 2004) as distinguished from the nutrientsmade essential by mutations conferring auxotrophic require-ments. When the growth of cultures (either steady state orbatch) is limited by phosphate, ammonia, or sulfate, unusedglucose is spared, as one might expect, whereas whengrowth is limited by auxotrophic requirements, excess glu-cose is completely consumed.

We interpret these results as reflections of system-levelregulatory mechanisms, as yet only partially understood,that must underlie the coordination of the growth rate withgene expression, entry into the cell division cycle, the stressresponse, and energy metabolism.

MATERIALS AND METHODS

Culture Conditions, Strains, and MediaYeast cultures were grown in chemostats under 36 different continuousculture conditions, namely, six different limiting nutrients each at six differentdilution rates. The dilution rates (and therefore the culture’s average expo-nential growth rate, �) ranged from �0.05 h�1 (corresponding to a celldoubling time of about 14 h) to more than 0.3 h�1 (doubling time of about2 h), and they were verified directly by collecting effluent into graduatedcylinders. Chemostat growth was limited by one of the following nutrients:glucose (G), ammonium (N), phosphate (P), sulfate (S), leucine (L), or uracil(U). Chemostats were established in 500-ml fermenter vessels (Sixfors; InforsAG, Bottmingen, Switzerland) containing 300 ml of culture volume, stirred at400 rpm, and sparged with five standard liters per minute humidified andfiltered air. Chemostat cultures were inoculated, monitored and grown tosteady state as described previously (Brauer et al., 2005). All cultures weremonitored for changes in cell density and dissolved oxygen and grown untilthese values remained steady for at least 24 h.

For nonauxotrophic limitations (G, N, P, and S), we used strain DBY10085(relevant genotype Mata MAL2-8C), which is the prototrophic CEN.PK-derived strain described by van Dijken et al. (2000). For limitations with uracil(U) or leucine (L), we used nonreverting mutant versions of the same strain,i.e., DBY9492 (ura3-52) or DBY9497 (leu2-3leu2-11), respectively.

Chemostat cultures were grown in minimal defined (MD) media supple-mented with glucose (G, N, P, and S limitations), L limitation, or U limitation.Concentrations of the limiting nutrient were adjusted downward in each MDmedium formulation. Detailed base media compositions are given in Table 1.These solutions were autoclaved and supplemented with glucose, metals, andvitamins (and necessary uracil or leucine), added via sterile filtration asdescribed previously (Saldanha et al., 2004).

Batch culture media were identical to chemostat media except that theycontained 1% glucose. Phosphate limiting medium contained a final concen-tration of 10 mg/ml potassium phosphate and was supplemented with either200 mg/l final leucine or 40 mg/l final uracil where appropriate. Uracillimiting medium contained 4 mg/l uracil, and leucine limiting media con-tained 40 mg/l leucine.

The patterns of gene expression in the chemostat under nutrient limitationclosely approximate the patterns found in batch cultures in the same mediumat the point that the concentration of the limiting nutrient falls to the valuefound in the corresponding chemostat (Saldanha et al., 2004; Brauer et al.,2005). Thus, there is a well-defined point of correspondence between thephysiology of the cells in chemostats and batch cultures in the same medium.

Measurement of Culture Growth ParametersAt each time point, 2 ml of culture was withdrawn and sonicated for 10 s, justenough to break up all clumps of cells, as confirmed in the light microscope.Sonicated cultures were examined under a light microscope at 200� magni-fication for identification of the proportion of cells with no buds, with smallbuds or with large buds. Culture density was measured both by absorbanceat 600 nm and with a Coulter counter (model Z2; Beckman Coulter, Fullerton,CA), set to count cells with volumes between 8.0 and 250.0 fl; data describingthe distribution of cell volumes also were recorded.

Residual glucose and ethanol concentrations were assayed as described byBrauer et al. (2005), and residual phosphate was measured as described bySaldanha et al. (2004).

RNA Isolation, Labeling, Microarray Hybridization,and Data CollectionSamples from chemostats (10 ml) were harvested for RNA by siphoningthrough a drop-tube followed by vacuum filtration onto nylon filters. Filterswere immediately placed into tubes containing liquid nitrogen and stored at�80°C until extracted for RNA.

RNA for microarray analysis was extracted by the acid-phenol method andcleaned using RNeasy mini columns (QIAGEN, Valencia, CA). RNA wasamplified and labeled using the Agilent low RNA input fluorescent linearamplification kit (P/N 5184-3523; Agilent Technologies, Palo Alto, CA). Thismethod entails initial synthesis of cDNA by using a poly(T) primer attachedto a T7 promoter. Labeled cRNA is subsequently synthesized using T7 RNApolymerase and either cyanine (Cy)3 or Cy5 UTP. Each Cy5-labeled experi-mental cRNA sample was mixed with the Cy3-labeled reference cRNA andhybridized were hybridized for 17 h at 60°C to an Agilent Yeast V2 oligomicroarray. Microarrays were washed, scanned with an Agilent DNA mi-croarray scanner (Agilent Technologies), and analyzed using Agilent FeatureExtraction Software version 7.5. Resulting microarray intensity data weresubmitted to the PUMA Database (http://puma.princeton.edu) for archivingand analysis.

Features flagged as outliers due to low intensity or poor quality wereexcluded, and the results for each gene, and time point were expressed as thelog2 of the sample signal divided by the signal in the reference channel. Thereference RNA for all samples was taken from the glucose-limited chemostatgrown at a dilution rate of 0.25 h�1.

Analysis of Gene Expression Data

Hierarchical Clustering. Expression data were clustered by gene, using theUPGMA algorithm of Eisen et al. (1998). Clusters with an average expres-sion that was either nutrient specific or correlated with growth rate wereidentified.

Table 1. Composition of chemostat media (values in grams perliter)

Compound

Limiting condition

G N P S L U

CaCl2�2H2O 0.1 0.1 0.1 0.1 0.1 0.1NaCl 0.1 0.1 0.1 0.1 0.1 0.1MgSO4�7H2O 0.5 0.5 0.5 0.5 0.5MgCl�6H2O 0.412KH2(PO4)2 1 1 1 1 1KCl 1(NH4)2SO4 5 5 5 5NH4Cl 4.05Glucose 0.8 5 5 5 5 5Leucine 0.015Uracil 0.005Vitamins and

metalsAs detailed in Saldanha et al. (2004)

Coordination of Growth Rate and Metabolism

Vol. 19, January 2008 353

Functional Annotation. Sets of genes were assigned process, function, andcellular components according to the annotations from the Gene Ontology(GO) (Ashburner et al., 2000). The significant representation of GO terms inthe set was evaluated by GO Term Finder at the Saccharomyces GenomeDatabase, and by the GO-TermFinder perl module (Boyle et al., 2004) usingthe Bonferroni-correct p value. Ontologies used were downloaded 7 August2007 from http://www.geneontology.org, and the GO gene associations forthe yeast genome were obtained from the Saccharomyces Genome Database(http://www.yeastgenome.org).

Singular Value Decomposition. We applied singular value decomposition (SVD)(Alter et al., 2000) to the expression data matrix to identify the major sources ofvariation in the data. Missing data were imputed using the k-nearest neighborsalgorithm (KNN imputation) (Troyanskaya et al., 2001), with k � 10.

Linear Regression Model for Gene Expression Data. For each of the resulting5537 genes, expression was individually modeled as a linear function ofgrowth rate. For each gene, this yielded a slope, baseline, and goodness of fit(R2); this slope measures the magnitude of the change in gene expression dueto growth rate. We computed p values to assess the significance of slopes andR2 values by using the bootstrap technique (Efron, 1993), and we corrected formultiple hypotheses using the False Discovery Rate procedure (Benjaminiand Hochberg, 1995). In each bootstrap replicate, a value was drawn atrandom, with replacement, from each of six sets of six columns (correspond-ing to chemostat cultures with the same flow rate, regardless of nutrientlimitation). The linear model described above was then applied to each of100,000 replicates, and the parameters describing slope and intercept wereretained; see Supplemental Table S1 for complete results. The analysis wasperformed using R (R Development Core Team, 2007) and MATLAB (Math-works, Natick, MA).

The distributions of regression slopes corresponding to lists of genes of interestwere compared with the bootstrap-generated null distribution. For each such list,a pair of p values was computed to assess the statistical significance of thecorresponding sensitivity to growth rate, using a Kolmogorov–Smirnov two-sample test and/or a Wilcoxon–Mann–Whitney two-sample test.

Tests for Correlation with Growth Rate. Genes were ordered by their bootstrapp value for the slope coefficient relating expression to growth rate. Thus, geneswith low ranks were those whose expression profiles correlated significantlywith growth rate, either positively or negatively. Bootstrap p values were alsocomputed for R2 to assess the significance of a linear response to growth, ascaptured by the regression model, as opposed to nonlinear response to growth,which we could not exclude a priori (see Supplemental Table S1).

Using these p values, we sought to identify a smaller set of genes that wasstringently defined as responding specifically to growth. To do so, we lookedfor genes whose response to growth was significant (either positive or nega-tive), whose response profile across flow rates was linear beyond chance, andwhose response did not change substantially across nutrient limitation re-gimes. Applying these filters generated a list of 72 genes (“calibration genes”in Supplemental Table S1).

Prediction of Relative Instantaneous Growth Rates. Relative instantaneousgrowth rates for novel microarray data were estimated with a linear modelcalibrated using the regression results from our nutrient limitation data.Specifically, the expression of gene g in microarray condition c was repre-sented as follows:

yg,c � bc � bg � rcxg � eg,c

The expression yg,c is thus a sum of a condition-specific baseline bc, a gene-specific baseline bg, a linear growth rate response with slope xg to the condi-tion’s chemostat flow rate rc, and an “error” term eg,c that captures leftovergene-specific variation (both biological and noise).

For any new microarray, the relative growth rate rc (along with the condi-tion-specific baseline bc) is unknown. We produce an estimate of the relativegrowth rate (and of the baseline) by leveraging the regression estimates (ofslope and gene-specific baseline) that were obtained for the 72 calibrationgenes (with bootstrapped p values �10�5 for both linear fit and slope) in ournutrient limitation data. By assuming an initial estimated baseline bc0 � 0, therelative growth rate and condition-specific baseline are estimated by itera-tively updating their values according to the following equations:

rct �

1|G|�

g�G

yg,c � bct � bg

xg

bct�1 �

1|G|�

g�G

yg,c � bg � rctxg

For further details, see (Airoldi et al., 2007).Complete data sets and supplemental materials are archived at http://

growthrate.princeton.edu.

RESULTS

To study, systematically and quantitatively, the effect ofgrowth rate on genome-wide gene expression, the cell cycle,and metabolism, we made measurements from 36 chemostatcultures, each of which was at steady state at one of sixdifferent growth rates ranging from from 0.05 h�1 (corre-sponding to a doubling time of about 14 h) to more than 0.3h�1 (doubling time �2 h). All were derivatives of strainCEN.PK growing in the same basic medium, but with one ofsix different growth rate-limiting nutrients: G, N, S, P, U (ina nonreverting ura3 mutant), or L (in a nonreverting leu2mutant).

The Fraction of Unbudded Cells Is Linear with GrowthRate for All Limiting NutrientsAs estimated by phase-contrast microscopy (and verified bymeasurements of DNA content in a fluorescence-activatedcell sorter; Supplemental Figure S1), the fraction of cells inan unbudded (G0 or G1) phase of the cell cycle was a linearfunction of the dilution rate D (u � 0.936–1.971D; R2 �0.836). The slope of the regression line does not vary signif-icantly between growth conditions (Figure 1A); thus, theexpectation of Unger and Hartwell (1976), that slower grow-ing cells spend an increasing proportion of the cell divisioncycle in G0/G1, was satisfied to considerable precision in allcases. Some previous studies (Rivin and Fangman, 1980;Guo et al., 2004) have found this expectation is not satisfiedin nitrogen limitation; we found no significant difference(Supplemental Figure S2). In our experiments, over a nearlysevenfold range of growth rates, yeast cells in balancedgrowth that grow more slowly spend quantitatively corre-spondingly larger fractions of the cell doubling time in theunbudded (G0/G1) phase of the cell cycle.

This result stands in contrast to the observation of(Saldanha et al., 2004), who found that in batch culturesstarving for phosphate or sulfate, cells accumulate in theunbudded state (G0/G1) within a cell generation of theexhaustion of the limiting nutrient, whereas batch cultureauxotrophs starving for leucine or uracil fail to show thisorderly response. Here, where cells are growing slowly butnot yet actually starving, we see that there is no difference inthe fraction of cells in G0/G1 in the chemostats: the samelinear relationship with growth rate was observed with alllimiting nutrients.

The other cell parameters were consistent with theoreticalexpectation (Kubitschek, 1970) and previous experience.With the exception of the glucose-limited cultures, cell den-sity is roughly a linear function of the dilution rate (Figure1B). The case of glucose is more complex, reflecting rela-tively well understood changes in glucose metabolism athigher steady-state growth rates (Kasper von Meyenburg,1969; Postma et al., 1989; Alexander and Jeffries, 1990). Av-erage cell volume varies across dilution rate in a complexmanner for all limiting nutrients (Figure 1C), with differ-ences that range between 16% (for sulfur) and 31% of themaximum (for phosphate and uracil). However, again withthe exception of the glucose-limited cultures, the calculatedtotal cell volume (average cell volume times number of cells)is proportional to the total cell mass (Supplemental FigureS3; R2 � 0.819).

Glucose Consumption and Ethanol Production inNonglucose-Limited Chemostats Depends on the Nature ofthe Limiting NutrientWe measured the residual glucose and ethanol in all 36chemostats, as described in the Methods. The results (Figure

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Molecular Biology of the Cell354

1D) for the glucose-limited chemostats were unremarkable:residual glucose was very low for all growth rates, and onlya very small amount of ethanol was produced (and that onlyat higher growth rates). In contrast, where glucose was notlimiting, there were striking differences. In the cases of lim-iting ammonia, phosphate or sulfate, high levels of glucose

remained, and relatively modest amounts of ethanol wereproduced. In the leucine- and uracil-limited chemostats, theresidual glucose was very low, and most of it seemed tohave been fermented to ethanol.

This bifurcation of response between phosphate or sulfatelimitation, on the one hand, and leucine or uracil limitation,

0.0

0.2

0.4

0.6

0.8

Unb

udde

d F

ract

ion

0

50

100

150

200

Cul

ture

Den

sity

(K

lett)

0

10

20

30

40

Ave

rage

Vol

ume

(fL)

G N P S L U

0

1

2

3

4

Glucose g/lEthanol g/l

[Glu

cose

] g/l

Dilution Rates [ 0.05, 0.1, 0.15, 0.2, 0.25, 0.3 h ] for each Nutrient Limitation Regime-1

A

B

C

D

Figure 1. Measured characteristics of cultures atsteady state. Limiting nutrients at bottom of fig-ure. Within each limitation, dilution rates are or-dered from 0.05 to 0.3 h�1 in 0.05 h�1 increments.(A) Fraction of unbudded cells. (B) Steady-stateculture density in Klett units. (C) Average cellvolume. (D) Residual glucose and ethanol levels.



on the other, corresponds to a difference observed previ-ously in batch cultures (Saldanha et al., 2004) found promptaccumulation (within a single cell cycle) of cells in G0/G1 inthe cases of limitation by phosphate or sulfate, but not byleucine or uracil. This result suggests that there are at leasttwo mechanisms that relate growth rate and metabolism:one that continuously controls entry into the cell cycle at lowgrowth rates, when cells are not yet starving, and anotherwhen cells actually exhaust their limiting nutrients. Thefailure to limit fermentation and spare the glucose in ourleucine and uracil chemostats, and the failure to promptlystop the cell cycle in batch cultures starving for leucine oruracil, may reflect a common signaling failure in case of theauxotrophic limitations.

We studied batch cultures to determine whether this in-ability to limit glucose consumption is a general phenome-non and not limited to continuous culture conditions. To thisend, we compared glucose consumption of auxotrophs andprototophs in batch cultures containing growth-limitingconcentrations of phosphate, leucine, or uracil (see Materialsand Methods for details). Growth was followed for 24 h, andthe glucose consumed was measured during late exponen-tial (t � 8 h) and stationary (t � 24 h) phases. The amount ofglucose consumed (normalized to cell number) was approx-imately twofold higher in auxotrophs that were starved fortheir auxotrophic requirement compared with either a pro-totrophic control or to the same strains starved for phos-phate and supplemented with ample leucine or uracil (Table2). Excess consumption of glucose was observed in the lateexponential and in the stationary phase of growth (Figure 1).In agreement with (Saldanha et al., 2004), we found that cellsgrown under these conditions do not mount an appropriatecell cycle arrest upon depletion of an unnatural limitation,but they do arrest in G1/G0 when supplemented with theirauxotrophic requirement and starved for phosphate (a nat-ural limitation; Supplemental Figure S2). Thus, glucosewasting in auxotrophs growth-limited for their requirementis not limited to continuous cultures, and this phenomenon,and the failure to arrest the cell cycle first noted in Saldanhaet al. (2004), is a feature of which essential nutrient is ex-hausted first and not of the genotype of the strain.

Growth Rate Accounts for a Large Fraction of the Signalin the Gene Expression PatternHierarchical clustering (Eisen et al., 1998) of gene expressionfrom the 36 chemostats is shown in Figure 2. Visual inspec-tion of Figure 2 shows a pattern that is strikingly similar forthe six different media, with large groups of genes thatincrease their expression with increasing growth rate, andcomparably large groups decreasing their expression withincreasing growth rate. In addition, there are much smallerclusters of genes that are expressed strongly in only one ortwo media; in general, these do not show as much relation-ship to growth rate. Fewer than 8% of the genes respond ina uniform, nutrient-specific manner (Figure 2). The largestnutrient-specific cluster, responding to phosphate limitation,comprises just 133 genes (2.4% of the total).

Singular value decomposition analysis (Alter et al., 2000)of these data are visualized in Figure 3A. The fractionalinformation in each eigengene (Figure 3B) shows that thefirst eigengene accounts for 43.6% of the variation in geneexpression present in the data set. The projection of thiseigengene correlates very strongly with the culture specificgrowth rate (R2 � 0.69; p � 10�9), indicating that a largefraction of the signal in gene expression is growth ratespecific. Figure 3C shows the average expression as a func-tion of growth rate for the first four eigengenes. From this,one can clearly see that expression of the first eigengene islargely independent of the nature of the limiting nutrient,whereas the second and third eigengenes show both stronggrowth rate correlation and nutrient specific effects, notablyfor phosphate (eigengene 2) and sulfate (eigengene 3) limi-tation. When we come to the fourth eigengene, very littlerelationship to growth rate remains. The sum of the infor-mation in the first three eigengenes amounts to nearly 70%of the total variation.

Expression of Many Genes Is Strongly Influenced byGrowth Rate to a Degree Characteristic for Each GeneFor each of the 5537 genes in the imputed data, expressionwas individually modeled as a linear function of growth rate(independent of limiting nutrient). Of these, 3049 genes(55.1%) have expression patterns than fit (at a bootstrappedp � 0.05) this linear model; of these, approximately half(1470, or 26.5% of all genes) have expression patterns thatrespond significantly (bootstrapped p � 0.05) to growth rate.

For those genes whose expression is correlated to growthrate, the magnitude of the effect of growth rate on geneexpression is given by the slope of the regression of expres-sion on growth rate. The distribution of these slopes (shownin Figure 4 as a histogram) is significantly broader than thenull distribution generated by bootstrap sampling (SD 2.97vs. 1.41). By plotting the positions of a set of genes on thishistogram, one can see systematic relationships between theaggregate response to growth rate and any other character-istic a query set of genes might share. In Supplemental TableS1 (see also http://growthrate.princeton.edu), we providedata for all the genes, including the significance with whichtheir expression correlates with growth rate. On the website,we also provide a simple utility that plots the distribution ofgrowth rate slopes for any query set of genes relative to theoverall distribution shown in Figure 4.

Functional Roles of Genes Strongly Correlated withGrowth RateTo identify the most prominent of the potential functionalreasons for the correlation between the expression of somegenes and the growth rate, we chose 1608 genes whose expres-

Table 2. Response to nutrient limitations in batch culture

StrainLimitingnutrient Supplement

Glucose8 h

Consumed24 h

% G0/G1

24 h

Prototroph Phosphate None 5.91 13.44 91leu2 Phosphate Excess leucine 5.04 10.15 93ura3 Phosphate Excess uracil 4.78 10.06 92leu2 Leucine None 10.22 18.70 60ura3 Uracil None 9.86 24.13 73

Batch cultures of isogenic CEN.PK derivatives were grown in che-mostat minimal medium containing 1% glucose with limiting phos-phate (10 mg/l), leucine (40 mg/l), or uracil (4 mg/l) supplementsas described in Materials and Methods. Excess leucine and uracil,when provided, was 200 and 40 mg/l, respectively. The growthcurves are shown in Supplemental Figure S3. Specific glucoseconsumption was calculated for time (t) as the normalized frac-tion of glucose consumed (grams per liter) using the equation(�glucose�initial � �glucose�t)/�glucose�initial)/cells/ml.

M. J. Brauer et al.


sion was best linearly correlated with growth rate (Supplemen-tal Table S2; see Materials and Methods for the details). Onesubset (337 genes) had negative slopes (more than 1.5 standarddeviations less than the average), another subset (291 genes)had positive slopes (more than 1.5 standard deviations morethan the average), and the third had low variability (boot-strapped p � 10�4) and low slope (within 0.5 SD of average),

i.e., their expression was not detectably related to growth rate(see the dash-dotted blue line in Figure 4).

Each of these subsets was submitted to GO Term Finder(Boyle et al., 2004) querying all three ontologies (Process,Molecular Function, and Cellular Component). The natureof the GO hierarchy produces highly redundant results inthis situation. To maintain only the biologically and statis-

Figure 2. Hierarchical clustering of expression values across dilution rates and limiting nutrients. Clustering by Pearson correlation revealsmany up- and down-regulated clusters spanning all nutrient limitations (e.g., Induced1, Induced2, Repressed) and few smaller gene groupsregulated in a nutrient-specific manner (e.g., G1–G4, P, S, and N). Reference for all samples is from a glucose-limited chemostat at 0.25 h�1.Conditions are as described in Figure 1.



Figure 3. SVD decomposition of expression data. Singular value decomposition of the growth rate/nutrient limitation microarray datashows that a large portion of the variation in gene expression (70%) is related to changes in growth rate. Secondary eigengenes also capturenutrient-specific responses (e.g., phosphate and sulfate). (A) 36 eigengenes. (B) Eigengene weights (eigenvalues). (C) Expression levels of thefour most significant eigengenes.

M. J. Brauer et al.


tically strongest relationships, we limited further analysis toGO terms with p � 10�3. These results were sorted by thefraction of genes hit within each GO term, and we focusedon the terms in which this fraction was at least 10%. The finalresult (Table 3 and Supplemental Table S2) gives a very clearpicture: the processes associated with the gene subset whoseexpression is negatively related to growth rate are focusedon energy metabolism, especially oxidative metabolism; theonly functional category that met our stringent criteria wasoxidoreducase activity, and the only cellular componentimplicated at this level of statistical stringency was the per-oxisome. Our negatively growth-correlated subset contained25 and 67% (designated term fraction in Table 3) of the genesannotated to peroxisomes and the peroxisomal matrix, re-spectively.

An equally clear picture emerged from the GO term anal-ysis of the subset of genes whose expression is positivelycorrelated with growth rate. About half of all the yeast genesassociated with mitochondrial protein import are found inthis subset, and substantial fractions of all the genes associ-ated with translation, ribosome biogenesis, and rRNA me-tabolism are represented. Consistently, ribosomal constitu-ents (mitochondrial as well as cytosolic) are very stronglyrepresented in both the Function and Component hierar-chies.

In contrast, the 980 genes whose expression is robustlyindependent of growth rate are annotated (with similar sta-tistical certainty and with similar Term Fraction values) tovery many (�80) diverse GO terms. The many processesthat underlie basic cytoplasmic cell biology or nonnucleolarnuclear biology are well represented in this subset of genes,i.e., those whose expression is unrelated to the growth rate.

Genes Whose Expression Is Correlated with Growth RateAre Highly Represented in the “Environmental StressResponse”One of the questions that can be addressed using the toolsdeveloped above is the relationship between growth rateand the many genes whose expression changes regardless ofthe nature of the environmental stress imposed. In their dataset of 156 such stress conditions, Gasch et al. (2000) foundtwo clusters of genes that were either induced or repressedtogether in this way, which they called the environmentalstress response (ESR) genes.

The distributions of the 283 genes in the ESR-inducedcluster (red) and the 585 genes in the ESR-repressed cluster(green) are superimposed on the histogram of expressionversus growth rate slopes in Figure 5. Both clusters had veryhigh representations of growth rate-correlated genes andconstitute sets of statistically significant outliers to the over-all distribution of slopes.

The 283-gene “ESR-induced cluster” has p values corre-sponding to Kolmogorov–Smirnov and Wilcoxon–Mann–Whitney two-sample tests practically equal to zero (see Ma-terials and Methods), indicating that this cluster has a verysignificant representation of genes whose expression is neg-atively correlated with growth rate. In fact, nearly one quar-ter of the top 500 genes with negative growth rate regulationare in the ESR-induced cluster found by Gasch et al. (2000).The remaining 376 genes are enriched for GO process anno-tation terms relating to carbohydrate metabolism, particu-larly respiratory metabolism and oxidative phosphorylation.The component annotation terms indicate a significant en-richment in genes for proteins localized to the lytic vacuoleand the peroxisome.

The “ESR-repressed” cluster (585 genes) also has Kolmog-orov–Smirnov and Wilcoxon–Mann–Whitney two-sampletest p values of approximately zero, indicating a highlysignificant positive correlation with growth rate. Again, the500 genes with the most significant positive correlationsbetween expression and growth rate include 227 of theESR-repressed genes. The remaining growth rate correlatedgenes are significantly enriched for GO process terms thatinclude membrane lipid biosynthesis and protein importinto the mitochondrion.

The most significant components of the first (growth ratecorrelated) eigengene (Figure 3) are also enriched for genesin the ESR. When genes were ranked by their projection ontoeigengene 1, a Wilcoxon-Mann-Whitney rank sum testshows that those genes identified by (Gasch et al., 2000) asbeing either induced or repressed in response to stress hada significantly lower than expected rank (t � 11.626, df �5535, p � 10�15). This is further evidence that the ESR genescontribute strongly to the first eigengene and therefore to thegrowth rate pattern seen in the expression data.

Not all the ESR genes are expressed in such a way as to besignficantly correlated with growth rate in our data. Wedetected no enrichment, for example, in genes for chaperoneproteins and for some other classes of classical stress re-sponse genes. The significant majority of stress-inducedgenes that are expressed at increasingly low growth rates arerelated to oxidative metabolism; of 131 genes, 16% are oxi-doreductases.

These results raise the possibility that many of the ESRgenes as defined previously may in fact not be respondingdirectly to stress, but instead are responding to a reductionin growth rate secondary to the stress. A similar suggestionhas recently been made in (Castrillo et al., 2007) based on asimilar set of observations.

Distribution of Slopes

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Figure 4. Distribution of experimental growth rate responses ver-sus bootstrapped background distribution. A histogram of the esti-mated regression slopes for 5537 genes is compared with a 100,000-point bootstrapped null distribution of slopes (density estimate;black, solid line) and to the distribution of slopes corresponding togenes that do not respond to growth rate (density estimate; dash-dotted, blue line). The expression responses of genes in our microar-ray data are significantly broader than expected by chance, whereasgenes we determine to be largely unresponsive to changes ingrowth rate have slopes near zero.



Table 3. GO annotation of genes according to growth rate response

Slope >1.5 SDs below average 337 genesProcess p value Gene hits Term size Term fraction (%)

Fatty acid �-oxidation 1.80E-04 6 8 75.0Glutamine family amino acid catabolic process 4.20E-04 7 13 53.8Energy reserve metabolic process 2.61E-05 12 36 33.3Glucose metabolic process 8.10E-04 14 65 21.5Monosaccharide metabolic process 1.10E-04 18 92 19.6Hexose metabolic process 9.50E-04 16 85 18.8Cellular carbohydrate metabolic process 7.75E-12 40 213 18.8Monocarboxylic acid metabolic process 5.86E-06 23 124 18.5Carbohydrate metabolic process 1.37E-12 43 233 18.5Energy derivation by oxidation of organic compounds 4.59E-06 25 143 17.5Generation of precursor metabolites and energy 5.02E-07 30 181 16.6Coenzyme metabolic process 1.40E-04 22 135 16.3Alcohol metabolic process 2.80E-04 24 163 14.7Carboxylic acid metabolic process 6.52E-05 37 312 11.9Organic acid metabolic process 6.52E-05 37 312 11.9

FunctionOxidoreductase activity 1.50E-07 38 270 14.1

ComponentPeroxisomal matrix 1.45E-06 8 12 66.7Microbody 3.53E-05 14 57 24.6Peroxisome 3.53E-05 14 57 24.6

Slope >1.5 SDs above average 291 genesProcess

Protein import into mitochondrial matrix 1.00E-07 11 22 50.0Maturation of SSU-rRNA 1.68E-10 17 44 38.6Protein import into mitochondrion 4.67E-07 13 37 35.1Protein targeting to mitochondrion 2.23E-05 13 49 26.5Mitochondrial transport 6.11E-05 14 62 22.6Ribosome biogenesis and assembly 4.73E-15 57 402 14.2Ribonucleoprotein complex biogenesis and assembly 2.20E-12 58 473 12.3Translation 8.47E-19 83 686 12.1rRNA metabolic process 8.51E-05 29 247 11.7rRNA processing 1.60E-04 28 240 11.7Macromolecule biosynthetic process 1.16E-19 97 881 11.0

FunctionsnoRNA binding 5.52E-06 11 32 34.4Structural constituent of ribosome 3.72E-43 71 230 30.9Protein transporter activity 2.10E-04 12 53 22.6Structural molecule activity 3.34E-30 72 357 20.2

ComponentMitochondrial outer membrane translocase complex 2.04E-05 6 8 75.0Cytosolic large ribosomal subunit (sensu Eukaryota) 3.72E-25 37 97 38.1Cytosolic small ribosomal subunit (sensu Eukaryota) 1.27E-15 24 64 37.5Cytosolic ribosome (sensu Eukaryota) 1.02E-43 64 176 36.4Cytosolic part 2.36E-41 65 197 33.0Large ribosomal subunit 8.13E-26 44 142 31.0Ribosomal subunit 4.18E-44 73 240 30.4Small ribosomal subunit 7.37E-16 29 98 29.6Ribosome 9.44E-38 80 357 22.4Small nucleolar ribonucleoprotein complex 3.39E-07 23 132 17.4Nucleolar part 4.92E-10 31 179 17.3Ribonucleoprotein complex 1.10E-35 101 623 16.2Nucleolus 1.44E-10 42 304 13.8Nonmembrane-bound organelle 1.96E-27 118 1033 11.4Intracellular non-membrane-bound organelle 1.96E-27 118 1033 11.4Cytosol 2.69E-13 69 626 11.0

Unresponsive genes 980 genesProcess

80 biological processes �1.00E-03 10.0Function

Exoribonuclease activity, producing 5-phosphomonoesters 6.60E-04 13 23 56.5Exoribonuclease activity 6.60E-04 13 23 56.5Exonuclease activity, active with either ribo- or deoxyribonucleic acids

and producing 5-phosphomonoesters8.10E-04 15 30 50.0

Guanyl-nucleotide exchange factor activity 7.40E-04 17 37 45.9General RNA polymerase II transcription factor activity 6.19E-05 25 62 40.3GTPase regulator activity 5.50E-04 27 77 35.1RNA polymerase II transcription factor activity 4.90E-04 37 123 30.1Transcription regulator activity 2.01E-09 90 327 27.5Protein binding 1.40E-04 121 585 20.7Hydrolase activity 1.61E-05 160 802 20.0

Component�40 cellular components �1.00E-03 10.0

M. J. Brauer et al.


Growth Rate and Cell Cycle-regulated GenesThe distribution of regression slopes of the 800 genes iden-tified by (Spellman et al., 1998) as having a strong cell cyclecomponent in expression was nearly identical to the distri-bution of slopes for all genes (Figure 5, black line). A break-down by cell cycle phase gives nearly identical results (Fig-ure 6), the exception being in the M-G1 phase, which is

slightly enriched for genes that have a negative correlationbetween expression and growth rate. Of the 89 M-G1 specificgenes, 24 have a growth rate dependence that is 1 SD fromthe mean of all genes. These results are consistent with theidea that slower growing cells spend more time waiting forSTART, i.e., in the M-G1 interval of the cell cycle.

A different picture emerges under the special conditionsof continuous culture that produce periodic cycles of me-tabolism (Tu et al., 2005; see also Kasper von Meyenburg,1969; Klevecz et al., 2004). Under these circumstances, ahigh degree of periodicity in expression is seen for morethan half of all yeast genes, vastly many more than the 800or so detected in synchronized cells growing under morestandard conditions (Spellman et al., 1998; Pramila et al.,2006; Kudlicki et al., 2007). It is of interest to see whetherthe several classes of genes distinguished by their relativeexpression during the metabolic cycling described andanalyzed by Tu et al. (2005) are correlated with growthrate in our chemostat steady-state conditions. In Figure 7,we plotted four sets of genes identified by (Tu et al., 2005)relative to the histogram of regression slopes introducedin Figure 4: the “most periodic” (Tu et al., 2005, their table2) and the mitochondrial ribosomal, peroxisomal, andcytoplasmic ribosomal clusters (Tu et al., 2005, their sup-plemental tables S1, S2, and S3, respectively). The resultsclearly show that the peroxisomal distribution (red line) isbimodal, with the majority class consisting of geneswhose expression is negatively correlated to growth ratein ordinary conditions (i.e., these genes, in ordinary con-ditions, are more strongly expressed at lower steady-stategrowth rates in all media we tested). The minority peakincludes some of the same ESR-induced genes that weidentified above as not changing with growth rate. The


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Figure 5. Transcriptional response of stress-related and cell cycle-related genes to changes in growth rate. Genes expressed periodi-cally during the cell cycle (black line; Spellman et al., 1998) aredistributed essentially as background, whereas genes induced (redline) or repressed (green line) by stress (Gasch et al., 2000) tend to beconversely repressed or induced as growth rate increases.


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Figure 6. Distribution of growth rate response slopes for genesspecific to individual cell cycle phases. A breakdown of cell cyclespecific gene response to growth rate by phase shows little variationfrom background. The 89 genes expressed in the M-G1 phase havea slight tendency to be down-regulated as growth rate increases.


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Genes in Table 2 (Tu et al., 2005)Genes in Table S1Genes in Table S2Genes in Table S3

Figure 7. Distribution of regression slopes for metabolic cyclingconditions of Tu et al. (2005). In our expression data, Tu et al.’s “mostperiodic” genes during metabolic cycling (their table 2; black line)are induced as growth rate increases, as are their mitochondrial andcytoplasmic ribosomal clusters (their supplemental tables S1 and S3;green and blue lines). Peroxisomal genes (their supplemental tableS2; red line) respond bimodally to growth rate, with the majorityshowing negative correlation and the minority not responding sub-stantially to growth rate (including several stress response genes).



other three groups, so clearly distinguished in the meta-bolic cycling conditions of (Tu et al., 2005), are all posi-tively correlated with growth rate under normal condi-tions (with a small subset of the ribosomal groupextremely strongly correlated with growth rate).

A Linear Model That Successfully Predicts Relative“Instantaneous Growth Rate” in Nonsteady-StateCulturesThe results of our study identify a number of genes (on theorder of one quarter of all genes in the genome) that arestrongly correlated with growth rate at steady state, regard-less of the limiting nutrient. Furthermore, there are manynonsteady-state conditions (notably the many stresses stud-ied by Gasch et al. (2000) and the several kinds of synchro-nized cultures) in which there seems to be a systematicrelationship to growth rate-related gene expression patterns.Indeed, these results encouraged the idea that much of thegene expression signature of “environmental stress” mightactually reflect a changing growth rate secondary to stress.It, therefore, seemed possible that one might use the patternof expression of a suitably chosen set of genes stronglycorrelated to growth rate as a way to estimate the instanta-neous growth rates of nonsteady-state cultures, even cul-tures in which the growth rate is changing rather quickly intime.

To this end, we produced a simple linear model (de-scribed in Materials and Methods) calibrated using the 72

genes best correlated to growth rate in our 36 chemostatsand least sensitive to nutrient-specific effects. We performeda number of cross-validation experiments on our chemostatdata to estimate the model’s expected error when inferringthe relative growth rate for a novel microarray (Supplemen-tal Figure S5).

We tested the model using the data from Brauer et al.(2005), which followed genome-wide gene expression dur-ing the diauxic shift from glucose fermentation to respira-tory growth on the evolved ethanol in batch culture. Theexperiments included measurements of residual glucose,ethanol, dissolved oxygen, and bud index. Brauer et al.(2005) found that the cells seem to stop growing, as judgedfrom a discontinuity in both dissolved oxygen and budindex, just when the glucose is exhausted at about ninehours after the beginning of their experiment. Figure 8shows the instantaneous growth rate inferred from ourmodel on the same axis used by Brauer et al. (2005). It is clearthat the inferred rate falls sharply at about this time and risesagain as the cells, following the shift, resume growing on theethanol. It is worth noting that Brauer et al. (2005) inter-preted their gene expression patterns in terms of an envi-ronmental stress response caused by the starvation.

DISCUSSION

We studied 36 yeast chemostat cultures growing at six dif-ferent growth rates under six different nutrient limitations:

7.25 7.5 7.75 8 8.25 8.5 8.75 9 9.25 9.5 9.75 10

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Figure 8. Inferred instantaneous growth rates in batch culture undergoing the diauxic shift. The main figure shows the relative growth ratesinferred by our linear model from microarray data in Brauer et al. (2005). The inset, from Brauer et al. (2005) demonstrates that their observedvariations in cell volume and dissolved oxygen exactly match our predicted cessation of growth as the diauxic shift occurs (�9.25–9.75 h).

M. J. Brauer et al.


glucose, sulfate, phosphate, ammonium, leucine (in a non-reverting leu2 mutant), and uracil (in a nonreverting ura3mutant). By using a variety of different nutrients to limitgrowth rate, we could focus on quantitative relationshipswith growth rate per se, and not with the particular nutrientregime that limits the growth rate. Our data agree very wellwith the results of others who have done similar studies(Boer et al., 2003; Saldanha et al., 2004; Regenberg et al., 2006;Castrillo et al., 2007), both with respect to genes that areresponsive to particular limitations and with respect togenes that respond mainly to growth rate.

Analysis of the small clusters of genes associated withparticular limitations basically recapitulates results obtainedpreviously by Saldanha et al. (2004). Most of the genesspecifically associated with sulfate, phosphate, uracil, orleucine limitation are readily understood in terms of knownmetabolic pathways and transport systems. The data and theanalysis of genes whose responses are specific to glucoseand nitrogen limitations also agree well with previous work(Boer et al., 2003; Regenberg et al., 2006; Castrillo et al., 2007).We do not discuss any of these further here.

Expression of About One Quarter of All Yeast Genes IsCorrelated with Growth Rate, but the Magnitudes of theSlope of the Relationship Are Characteristic for EachGeneBy a statistical analysis, we identified a large number ofgenes (�27% of all yeast genes) each of whose expression islinearly correlated (either negatively or positively) with thegrowth rate, independent of the limiting nutrient. Some ofthese genes were much more strongly affected by growthrate than others, again independent of the identity of thelimiting nutrient. Both hierarchical clustering and SVD anal-ysis of the entire chemostat data set indicates that the cor-relation between the steady-state level of mRNA and thenominal growth rate applies to many genes.

Castrillo et al. (2007) recently published a set of dataentirely consistent with the data set presented here for glu-cose, nitrogen, sulfur, and phosphate limitations. AlthoughCastrillo et al. (2007) explored some very similar experimen-tal conditions, they took a technology survey approach thatincluded proteomic and metabolomic data in addition togene expression levels. Their analysis is focused on theidentification and behavior of individual genes (e.g., TOR1)that regulate pathways involved in growth regulation,whereas we attempted a system-level description of therelationship between growth rate and gene expression, con-trol of the cell cycle, and metabolism. To this end, we com-bined traditional observation-based data analysis, includingclustering and decomposition techniques, with a statistical,model-based study of our gene expression data. The fact thatmany genes are expressed in a way correlated with growthrate, independent of the identity of limiting nutrient,emerged as a strong conclusion from both studies.

To gain a deeper and less descriptive understanding of thebiological roles of genes whose expression level correlateswith growth rate per se, we introduced another level ofanalysis. We took advantage of the observation that expres-sion of some genes changes more profoundly with differ-ences in growth rate than others (i.e., the slope of the regres-sion varies from very negative to very positive). We didextensive bootstrap analysis to determine the statistical sig-nificance of the slopes, because correlation itself will natu-rally be stronger when the slope is steeper: the bootstrap pvalues indicate how robust the determination of the slope isstatistically.

The combination of each gene’s growth rate slope (i.e.,strength of transcriptional response) and the bootstrap pvalues of these slopes (i.e., their statistical significance),given in Supplemental Table S1 for all genes, allows therigorous identification of genes responding strongly togrowth rate in a nutrient-independent manner. A histogramof the slopes for all yeast genes allows one to visualize thegrowth rate sensitivity of a single gene or a list of genesrelative to the overall distribution (Figures 5–7). These meth-ods (also available at http://growthrate.princeton.edu) fa-cilitate the use of the information from this data set to makeinferences for our own analysis, and to analyze the results ofothers (see below).

To focus on the biology of gene expression as a function ofgrowth rate, we defined (see Materials and Methods for sta-tistical detail) a subset of 1,608 genes that correlate with acharacteristic slope: 337 had a negative slope, 291 a positiveslope, and 980 a slope near zero (i.e., their expression wasroughly the same at all growth rates). The point to be em-phasized here is that this stringent a selection of 337 � 291 �628 (i.e., �10% of all yeast genes) necessarily underestimatesthe number of genes with nonzero slopes, because geneswith smaller (positive or negative) slopes and/or noisy dataare likely to fail the statistical tests. The SVD and clusteringestimates (which suggest larger numbers of growth rateresponsive genes) are surely closer to reality; we, therefore,suggest that expression of at least 27% of yeast genes iscorrelated with the nominal growth rate in chemostats, re-gardless of the nature of the limiting nutrient.

Functional Roles of Genes Whose Expression Is MostStrongly Related to Growth RateGO Term Finder analysis of the subsets of genes with well-defined slopes (Table 3 and Supplemental Table S2) presentsa very clear picture. The positive-slope subset of 291 genesfocuses on the translation machinery, both cytosolic andmitochondrial. This result has very strong precedents inthe literature of both bacterial and yeast physiology, wherethe correlation between the number of ribosomes and thegrowth rate was noted very early (Maaloe and Kjeldgaard,1966; for more recent reviews, see Nomura, 1999; Warner,1999; Zhao et al., 2003). The biological logic for this relation-ship is virtually self-evident: to grow at a faster rate, moreproteins must be made per unit time, which is facilitated byhaving more ribosomes per cell.

Many different regulatory mechanisms (most prominentamong them the TOR1 signaling system) have been impli-cated in this connection (for review, see De Virgilio andLoewith, 2006a,b). Of particular relevance are the results ofJorgensen et al. (Jorgensen et al., 2004; Jorgensen and Tyers,2004), who found a connection between ribosome biosyn-thesis and cell cycle entry at START (Hartwell, 1974; Hart-well et al., 1974) via the regulation of both processes by theproducts of SFP1 and SCH9.

The negative-slope subset of 337 genes relates to functionsassociated with oxidative energy metabolism, especiallythose carried out in peroxisomes. Peroxisomes have beenassociated with fatty acid metabolism, with oxygen metab-olism (particularly reactive oxygen) and, more recently, withautophagy (for reviews, see Kim and Klionsky, 2000; vanRoermund et al., 2003; Monastyrska and Klionsky, 2006;Rottensteiner and Theodoulou, 2006; Wanders and Water-ham, 2006). The biological logic here is less obvious, al-though the benefits of engaging in autophagy and degrada-tion of cellular materials during nutrient limitation are clear.Another possibility relates to the metabolism of reactiveoxygen species, for which there might be more need when



time between cell division cycles is longer. A purely meta-bolic logic (e.g., a need for more beta-oxidation of fatty acidsat slow growth rates) is more difficult to rationalize. Al-though reasonable when carbon (in our case glucose) islimiting, it is not obvious how this might work for the otherlimitations, especially those that leave high concentrations ofresidual glucose in the medium at steady state.

The statistically derived growth rate-independent subset(980 genes) is, in this context, equally informative. It in-cludes a large number of GO terms that cover much of theremaining yeast cell biology. These 84 GO process termsnotably include such areas as transcription, DNA metabo-lism, chromatin remodeling, proteolysis, protein secretionand even the cell cycle, among many others (SupplementalTable S2 shows an even larger diversity at only slightlylower p values).

The Idea of an Instantaneous Growth RateIn previous publications (Saldanha et al., 2004; Brauer et al.,2005), we showed that the overall pattern of gene expressionin chemostats closely approximates that found in batch cul-tures that are running out of the same limiting nutrient. Atabout the time that the residual level of the limiting nutrientin the batch culture reaches the level found in the corre-sponding steady-state chemostat, the pattern of gene expres-sion in batch approaches that of the chemostat culture. Thesimplest interpretation of these results is that somehow thecells have a way of sensing their instantaneous growth rate.This interpretation is fortified by our ability to predict, witha simple quantitative linear model, the instantaneousgrowth rate of a batch culture undergoing the diauxic shift(Figure 8). Our predictions correspond well to the variationsin dissolved oxygen that were measured at the time byBrauer et al. (2005).

The mechanism(s) that underlie this coordination of geneexpression must be largely independent of the nature of thegrowth limitation and also must require very little time toexecute relative to the doubling time. The entire fall andresurgence of the growth rate in the diauxic shift experimentcovers less than a doubling at the fastest rate on glucose. Inthis context, it is very interesting to note that the GO terms(mainly ribosomal functions) for our positively correlatedgene set corresponds almost exactly to the set identified byGrigull et al. (2004) in their study of genes regulated post-transcriptionally by mRNA stability. It is entirely possible toimagine that when growth slows for any reason, even tran-siently, translation rates fall concomitantly, and the mRNAsjointly identified by Grigull et al. (2004) and by the dataprovided here become almost immediately unavailable. Theconcentration of one or more of these RNAs might, directlyor indirectly, be the carrier of the information that signalsthe instantaneous growth rate to other cellular regulatorysystems.

The ability to estimate instantaneous growth rates frompatterns of gene expression could turn out to be a usefultool. Because it seems that one can estimate this parameter indiverse media and in batch cultures where the growth rate ischanging (and in continuous cultures), it may be a usefultool for normalizing quantitative comparisons among exper-iments done under different conditions (which may other-wise give results that are systematically biased because ofdifferences in growth rates).

Instantaneous Growth Rate and the Environmental StressResponseAmong the positively correlated genes, we found many (butnot all) of the genes whose expression declined during the

environmental stress response as defined by (Gasch et al.,2000); among the negatively correlated, we found many (butnot all) of the genes whose expression increased in the Gaschexperiments. Similar data were reported recently in Castrilloet al. (2007). A connection between growth rate and stressresistance has experimental precedent: Elliott and Futcher(1993) found that yeast grown in batch at slower growthrates by using relatively poor sources of carbon or nitrogenare more resistant to stress, which one might infer to meaninduction of the stress-response genes. Much more recently,gene expression data consistent with such a connection havebeen reported by Slattery and Heideman (2007).

These results raise the possibility that much (but probablynot all) of what has been defined as environmental stressresponse might equally well be thought of as a generalresponse to changes in the instantaneous growth rate. Be-cause it consists mainly of the most growth rate-sensitivegenes, much of the response could be secondary to a muchsmaller number of specific responses to individual environ-mental stresses. It also is worth noting here that the steadystate mRNA concentrations of the positively growth rate-correlated genes fall remarkably rapidly after applications ofstresses (Gasch et al., 2000), consistent with the idea of reg-ulation at the level of mRNA degradation (Grigull et al.,2004) and transcription.

It may well turn out that regulatory mechanisms and evenactual regulators are shared and overlap between responsesto specific stress and simple reductions in instantaneousgrowth rate.

At Least Two Mechanisms Must Exist Connecting Entryinto the Cell Division Cycle with MetabolismWe found a simple linear relationship, again independent ofthe limiting nutrient, between steady-state growth rate and thefraction of unbudded (i.e., G0/G1) cells, consistent with thehypothesis (first proposed by Unger and Hartwell, 1976)that at reduced growth rates, yeast cells spend correspond-ingly increased amounts of time in the phase of the cell cyclejust before “START” (i.e., the activation of the cyclin-depen-dent kinase Cdc28p; Pringle and Hartwell, 1981). This rela-tionship holds for all nutrient limitations and accords gen-erally with current views of cell cycle regulation (e.g., Laabset al., 2003; Verges et al., 2007; for recent reviews, also seeFutcher, 2002; Jorgensen and Tyers, 2004; Schneider et al.,2004; Bloom and Cross, 2007). Our observations support amechanism that is independent of the nature of growthlimitation. The classical model wherein START is passedwhen the cyclin/DNA ratio is above a threshold is such amodel, and it is consistent with these data.

However, the results from batch cultures cannot be ex-plained so simply. As found in Saldanha et al. (2004), weagain observed that ura3 or leu2 auxotrophs depleted oflimiting uracil or leucine do not properly arrest growth in anunbudded state, whereas the same strains will arrest prop-erly when limited on phosphate with excess uracil or leucine(Table 2). This result is not easily reconciled with the classi-cal models; indeed, it is in apparent conflict with the obser-vation that these same auxotrophs limit entry into the cellcycle in just the same way as do prototrophs in limitingglucose, ammonia, phosphate or sulfate (which we call nat-ural nutrients, after Saldanha et al., 2004).

This result is made more interesting by our additionalremarkable observation, in both batch and continuous cul-tures, that excess glucose is spared when cultures limit onthe natural nutrients, whereas it is fermented completely toethanol when cultures are limited by auxotrophic require-ments. The combination of a defective regulation of the cell

M. J. Brauer et al.


division cycle with uncontrolled glucose fermentation isreminiscent of the “Warburg effect” in human cancer cells.(Warburg, 1956) reported a now general observation thatmost human cancer cells, even under aerobic conditions,will exhaust the glucose in their medium by fermentation tolactate, whereas normal cells and tissues will spare the glu-cose (for review, see Kim and Dang, 2006).

Together, these results point to the existence in Saccharo-myces cerevisiae of at least two regulatory systems that func-tion in coordinating growth rate, cell division, and metabo-lism. One of these, which seems to be independent of thetype of nutrient limitation, seems to continuously limit entryinto the cell cycle based on the growth rate without produc-ing a full cell cycle arrest. This could be the mechanismenvisioned in the classical models. The other, which webelieve functions only when a natural nutrient is totallydepleted, seems to cause a more complete cell cycle arrest inbatch cultures and, we suggest, may also act to preventunlimited fermentation of any remaining glucose.

We suggest that both of these mechanisms must somehowrespond to the instantaneous growth rate: one acts in agraded manner limiting cell cycle entry, and the other actsonly when starvation is imminent.

Is There a Connection between Growth Rate Controland the Metabolic Cycling Phenomenon?One of the more surprising results we obtained is that of the�800 genes that seem to be periodically expressed duringcells synchronized in all the standard ways (Spellman et al.,1998; Pramila et al., 2006), relatively few were strongly cor-related to growth rate with steep slopes. Because there issuch a large difference in the fraction of cells in G0/G1 atlow growth rate compared with high, we anticipated that wemight see more than the relatively modest enrichment wefound in the genes whose mRNA abundance peaks in M/G1(Figure 6). What was not observed by Spellman et al. (1998)or Pramila et al. (2006) when they synchronized cells withmating factors, drugs or cdc mutants, was periodicity ofexpression of the several major classes of genes we foundstrongly correlated, negatively or positively, with growthrate.

A similar analysis using the data of Tu et al. (2005), whichderives from cultures synchronously undergoing metaboliccycling, produced a completely different picture (Figure 7),even though they used the same CEN.PK strain we used.Many (800) genes are periodically expressed in the meta-bolic cycling regime. There seems to be a striking concor-dance between the sets of genes that Tu et al. (2005) seestrongly expressed during the several phases of their meta-bolic cycle and the subsets of genes we defined as beingmost correlated with growth rate. It is important to note thatin all the metabolic cycling experiments, the genes that areperiodic under the standard synchronization conditions aregenerally also periodically expressed, with periods synchro-nized to the metabolic cycles (Klevecz et al., 2004; Tu et al.,2005; Kudlicki et al., 2007). The set of genes associated withthe “oxidative phase” of the metabolic cycle is bimodal inFigure 7, but the majority of the genes are the same onesassociated with the peroxisome and its metabolic functions.The sum of all the genes associated with the other phasesroughly comprises our gene subset whose expression ispositively correlated with growth rate and whose functionsare strongly associated with the cytoplasmic and mitochon-drial translational machinery.

What are we to make of this concordance? One simplehypothesis, which is quite testable, is that there is a meta-bolic cycle under all conditions, but only under the condi-

tions used by Tu et al. (2005) and Klevecz et al. (2004) doentire cultures become synchronous, possibly because ofchanges in the medium (e.g., dissolved oxygen, pH, andresidual glucose). The only immediate difficulty with thishypothesis is that synchronization of the cell division cycleunder the classical conditions, in several laboratories, pro-duced no sign of synchronization of expression of the char-acteristic subsets of genes found during metabolic cycling(Tu et al., 2005), stress response (Gasch et al., 2000), or bycorrelation with growth rate in continuous culture (Castrilloet al., 2007; this study).

Another way to look at the problem, which is more diffi-cult to test, is to suppose that the conditions of metaboliccycling involve changes in the extracellular medium, asdescribed above, that result in changes in the instantaneousgrowth rate. This would result in periodicity of the genesstrongly correlated to the instantaneous growth rate. Thesuggestion by Futcher (2006); compare (Kuenzi and Fiechter,1969; Kasper von Meyenburg, 1969), which posits that cellsuse accumulated stores of fermentable sugar to provide a“finishing kick” to metabolism that allows the cells to passSTART, is a nice variant of this idea.

Both Tu et al. (2005) and others (Futcher, 2006; Chen et al.,2007) imagine that some or all of the evolutionary pressurethat results in metabolic cycling might be driven by the needto minimize (or avoid entirely) the damage to DNA from theinevitable reactive oxygen by-products of respiratory metab-olism. The prominence of genes associated with peroxisomalfunctions supports such a proposal. Lower growth ratesrequire longer exposure to oxidative metabolism in order toproduce enough energy, and this might be the reason thatgenes encoding the peroxisomal functions are preferentiallyexpressed.

CONCLUSIONS

We have shown that a large fraction of all yeast genes areexpressed to a degree that is linearly related to the growthrate, regardless of the nature of the limitation on growth.The slopes, indicating the relation of each gene’s expressionto growth rate, can be used to evaluate the likelihood thatchanges in gene expression might be related to changes(apparent or not) in growth status of yeast cells. On thisbasis, we have found that there may well be changes in whatwe define as instantaneous growth rate in cells undergoinga stress responses or metabolic cycling.

In the Supplement Material and on our website http://growthrate.princeton.edu, we provide, in addition to an ex-tensive new expression data set, growth rate sensitivity in-formation for every yeast gene. We also providecomputational tools that allow these tables to be used toevaluate other data sets even when the growth rate is chang-ing, uncertain, or unknown.

We also describe a new phenomenon in yeast, analogousto the glucose wasting Warburg effect in cancer cells. Auxo-trophs starving for their growth requirements waste glucoseand fail to arrest properly at G0/G1. Neither phenotype isseen when the same cells are starved for phosphate or sul-fate. We interpret these results as indicating that there mustbe at least two mechanisms that connect metabolism andentry into the cell division cycle, both of which must some-how sense the instantaneous growth rate.

ACKNOWLEDGMENTS

We thank Maitreya Dunham and Sandy Silverman for technical advice andChad Myers, Matthew Hibbs, and Florian Markowetz for insightful discus-



sions. Research was supported by the National Institute of General MedicalSciences Center for Quantitative Biology (GM-071508) and individual grantsGM-46406 (to D.B.); National Institutes of Health grant R01 GM-071966,National Science Foundation (NSF) grant IIS-0513352, and NSF CAREERaward DBI-0546275 (to O.G.T.); and fellowship grant HG-002649 (to M.J.B.).

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